I have had both in my hands at the same time. I attempted to swap the non cooler version for a spare that has the cooler in it. That was two years or so back. The simple filter mount adapter can be removed, with great difficulty. But the one with the cooler cannot be installed without also R&Ring the water pump with it.
The short hose is way too short to be able to install separately, and I couldn't put the adapter on with the hose at the same time. I can't explain that fully, just that you can only get one hand in there to both hold the adapter, and tighten the bolt at the same time.
The two adapters are identical on the engine side, they use the same mounting bolt, and the same o-rings.
If you set about removing the adapter, remove as much around that as possible, first. I'd take off the sway bar if I did it again, and maybe loosen the steering rack. There is almost no room in there to get at the mounting bolt with your hand and a tool. I dislike that adapter big time.
I suggest trying a different adapter, FMS makes one that can rotate any amount, and mounts a little closer to the engine. If it will clear and be easier to R&R, that would be worth the $85 price. That one is also made for an old block thread adapter(the FL1A version), and it takes an FL1A filter. The block adapter requires a large Allen wrench to remove it, it's about 1/2" or so in size. I used a chisel back end to check the size one time, I've forgotten what it was.